Left-arm spinner Ashton Agar is the latest Australia squad member to return home from the Test series in India having been deemed surplus to requirements.

Agar, 29, had been overlooked for selection in the first two Tests as India claimed a 2-0 lead to retain the Border-Gavaskar Trophy.

The left-armer had played in Australia's final Test of the home summer against South Africa in Sydney but fell down the spin pecking order after a poor display where he failed to take a wicket.

Spinners Nathan Lyon, Todd Murphy and fellow left-armer Matt Kuhnemann have all been used in India and Agar has been let go with leggie Mitch Swepson returning to the set-up after flying home for the birth of his first child.

Kuhnemann had been called into the squad when Swepson exited and leaped Agar for a spot in the XI for the second Test.

After losing the second Test by six wickets on Sunday, Josh Hazlewood and David Warner both exited the Australia camp due to injuries, while captain Pat Cummins flew back to Sydney for a family health issue.

Agar's departure will enable him to link up with Western Australia to play in the Sheffield Shield and their upcoming Marsh Cup final. He is likely to be part of Australia's ODI squad for the series in India from March 17 to 22 after the Tests.